# Probability and Statistics

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1. Suppose the hourly wages of all workers in a manufacturer company have a normal distribution with a mean of \$15.50 and a standard deviation of \$2.75. If we randomly select a sample of 10 workers from this company, find the probability that their mean hourly wage is:
1. Less than \$14.25

1. More than \$16.50

1. Suppose the monthly salary of teacher with no more than 5 years teaching experience in California follows a normal distribution with the mean of \$6250 and standard deviation of \$320.
1. What is the probability that a randomly selected teacher with no more than 5 years teaching experience in California makes less than \$6000 or more than \$6500 per month?

1. Find a range of salaries, rounded to the nearest ten, that separates the middle 80% from the rest.

1. Samsung TV have normal distribution of no repairs time with the mean of 9.5 years and standard deviation of 1.75 years. If we randomly select 1 Samsung TV, find the probability that
1. No repair is needed between 5 to 9 years.

1. Find two values that separates the middle 60% from the rest

1. If we randomly select 4 such TVs, find the probability that their mean is above 8.

1. A loaded coin with .65 probability of tails is tossed 800 times. Find the following:
1. n=
2. p=
3. q=
4. μ=
5. σ2=
6. σ=
7. Find P(number of tails is at least 460)

1. Estimate Pnumber of tails is at least 460 using normal distribution.

1. Use a uniform probability distribution for all values from 20 to 50.
1. Draw and label

1. Find P(x=25)

1. Find P(x<25.5 or x>35)

1. Find two values that separates the middle 60% from the rest

1. Suppose you buy 1 ticket for \$1 out of a lottery of 1,000 tickets where the prize for one winning ticket is to be \$500. Find the expected value.

1. Given the following probability distribution table,
 x P(x) 1 .12 2 3 .3 4 .23 5 .12
1. Find P(x=2)

1. Draw and label probability distribution histogram

1. Find μ and σ

1. Find the exact value for σ2

1. Use one decimal place to find the usual range

1. Suppose there are 10 females and 15 males. Select 3 people.
1. How many ways can we select 3 people?

1. How many ways can we select 3 females?

1. Find P(3 females)

1. How many ways can we select 2 females? Keep in mind, we must select 3 people.

1. Find P(2F and 1M)

1. P(1F and 2M)

1. P(0F and 3M)

1. Suppose PA=.7, PB=.3, A&B are I.E.
1. Find P(A and B)

1. Find P(A or B)

1. Make venn diagram

1. Find PAB=

1. Find PBA=

1. nswer the following questions given the table below .

Do you drink?

 Freq Yes No Total Males 17 23 40 Females 20 40 60 Total 37 63 100

1. Find PMY

1. Find P(N|F)

1. Find P(Male or no)

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